How to connect an old motherboard with a 12 pins power connector?

EDIT: I appreciate all the thumbs ups, but as other users have pointed out this is likely not an AT connector. After doing more research, my best suggestion to the OP is to purchase the original part number item to insure compatibility with this system. There are no second chances, once the wrong power supply is plugged in, the motherboard is toast.

It appears, based on research, that this system is a Compaq Presario 22xx series. The specs of that series, and references to the original power supply part number suggest that this is an ATX style power supply. The extra 6-pin plug is typically an auxiliary connection. However, it is highly likely, as suggested by other commentators that this is a completely proprietary power supply. A lot of manufacturers are guilty of creating non-standard systems around this era. I cannot find any standard power supplies that used 12 pin AT/PC style power connectors and a 6-pin auxiliary connector. What is for sure, is that this power supply (not clearly seen in the OP's photo) is also proprietary in shape and size:

So, I have left the original message below, but I think it is prudent to not take chances given the sensitive nature of this repair. Just spend the money on getting the exact original part number.

----- ORIGINAL ----- The connector on your motherboard is an AT connector. The power supply you are trying to hook up is an ATX connector.

You'll need to buy an AT power supply. When you hook it up make sure you attach the two motherboard power connectors with the black wires next to each other.

http://wiki.robotz.com/index.php/PC_Power_Supply_Voltage_Data_and_Connector_Types

Now, I have to ask - What are you doing with this computer from 20+ years ago?

As mentioned in the other answer that is an old AT style power connector.

It is possible to connect an ATX power supply using an adapter but there are a couple of caveats.

1. Your system may need -5V which modern ATX PSUs don't have (some but not all older ones do)
2. AT power supplies are not controlled by the motherboard but by a seperate power switch. The adapter is likely to have a pair of wires for connecting to your power switch. Depending on your case design you may be able to hook up the existing power switch or you may need to fit a new one to the case somehow.

This is neither ATX nor AT power supply. The 2 main plugs (P8 and P9) are regular AT, but there is also an unaccounted for third one and PSU provides +3.3V and +5VSB rails which is something that AT PSUs don't do. Also, it doesn't have -5V rail, which regular AT should have.

My guess is that's an intermediate-era PSU, which internally is ATX (hence the ATX-like configuration of lines), but uses 2 AT-style connectors + a proprietary 3rd one. Your best bet IMHO is to seek help from some hacker with basic soldering skills. Cables from the dead one could most likely be combined with a working ATX PSU to get an operational replacement.

There is a possibility that the 3rd connector is P10/P11 which supplies 3.3V, but if that's the case, where does +5VSB line go? You can buy an ATX to AT-with-P10 adapter, but if the 3rd one is not P10 but proprietary (with +5VSB), it can end badly.

Try asking at https://retrocomputing.stackexchange.com, maybe someone will recognize the setup. But provide better pictures of the plugs and motherboard, with visible cable color configuration and markings.

A quick google search will soon give many results for AT power supplies Adaptors for ATX seem quite mad, particularly given that:

The machine is for a control machine, so Im assuming that there is an (ISA?) card interfacing the hardware. There may be a custom BIOS for the control card making moving it very difficult.

Add in cards may need -5 V even if the motherboard doesn't need it to boot, so if you try converting an ATX PSU be prepared for the machine to not control anything, even if it powers. Like the other answers say, get an AT power supply.

I'd also image the hard drive whilst I was about it so this can be replaced if it goes.

EDIT After seeing the other answer, that this is neither AT or ATX, a google search of the part number on the PSU indicates this came from a Compaq Presario. Those things use ATPWR psu, so you'll need a compaq power supply - completely non standard.